Jordan structures of strictly lower triangular completions of nilpotent matrices
type: Item
instance of: scholarly article
title: Jordan structures of strictly lower triangular completions of nilpotent matrices
zbMATH Open document ID: 0839.15005
DOI: 10.1007/BF01203918
author: Mark Krupnik
author: A. Leibman
published in: Integral Equations and Operator Theory
publication date: 1996-06-19T00:00:00Z
review text: The authors prove the following theorem conjectured by \textit{L. Rodman} and \textit{T. Shalom} [Linear Algebra Appl. 168, 221-249 (1992; Zbl 0748.15011)]: Let \(A\) be a nilpotent \(n \times n\) matrix with Jordan blocks of size \(q_1 \geq \cdots \geq q_s\). If \(p_1 \geq \cdots \geq p_r\) is a sequence of positive integers that majorizes the sequence of \(q\)'s (i.e. \(r \leq s\), \(p_1 + p_2 + \cdots + p_t \geq q_1 + q_2 + \cdots + q_t\) for \(t = 1, \dots, r\), and \(p_1 + \cdots + p_r = q_1 + \cdots+q_s)\), then there exists a strictly lower triangular matrix \(T\) such that \(A + T\) is nilpotent and the \(p\)'s are the sizes of the Jordan blocks of \(A + T\).
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 838571
zbMATH Keywords: Jordan structures
zbMATH Keywords: strictly lower triangular completions
zbMATH Keywords: nilpotent matrices
reviewed by: Rabe von Randow
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 838571